/// <summary>
/// Computes the "stress" of the current layout of the given graph:
///
/// stress = sum_{(u,v) in V} D(u,v)^(-2) (d(u,v) - D(u,v))^2
///
/// where:
/// V is the set of nodes
/// d(u,v) is the euclidean distance between the centers of nodes u and v
/// D(u,v) is the graph-theoretic path length between u and v - scaled by average edge length.
///
/// The idea of “stress” in graph layout is that nodes that are immediate neighbors should be closer
/// together than nodes that are a few hops apart (i.e. that have path length>1). More generally
/// the distance between nodes in the drawing should be proportional to the path length between them.
/// The lower the “stress” score of a particular graph layout the better it conforms to this ideal.
///
/// </summary>
/// <param name="graph"></param>
/// <returns></returns>
public static double Stress(GeometryGraph graph)
{
ValidateArg.IsNotNull(graph, "graph");
double stress = 0;
if (graph.Edges.Count == 0)
{
return(stress);
}
var apd = new AllPairsDistances(graph);
apd.Run();
var D = apd.Result;
double l = graph.Edges.Average(e => e.Length);
int i = 0;
foreach (var u in graph.Nodes)
{
int j = 0;
foreach (var v in graph.Nodes)
{
if (i != j)
{
double duv = (u.Center - v.Center).Length;
double Duv = l * D[i][j];
double d = Duv - duv;
stress += d * d / (Duv * Duv);
}
++j;
}
++i;
}
return(stress);
}
/// <summary>
/// Layouts a connected graph with Multidimensional Scaling, using
/// shortest-path distances as Euclidean target distances.
/// </summary>
/// <param name="geometryGraph">A graph.</param>
/// <param name="settings">The settings for the algorithm.</param>
/// <param name="x">Coordinate vector.</param>
/// <param name="y">Coordinate vector.</param>
internal static void LayoutGraphWithMds(GeometryGraph geometryGraph, MdsLayoutSettings settings, out double[] x, out double[] y)
{
x = new double[geometryGraph.Nodes.Count];
y = new double[geometryGraph.Nodes.Count];
if (geometryGraph.Nodes.Count == 0)
{
return;
}
if (geometryGraph.Nodes.Count == 1)
{
x[0] = y[0] = 0;
return;
}
int k = Math.Min(settings.PivotNumber, geometryGraph.Nodes.Count);
int iter = settings.GetNumberOfIterationsWithMajorization(geometryGraph.Nodes.Count);
double exponent = settings.Exponent;
var pivotArray = new int[k];
PivotDistances pivotDistances = new PivotDistances(geometryGraph, false, pivotArray);
pivotDistances.Run();
double[][] c = pivotDistances.Result;
MultidimensionalScaling.LandmarkClassicalScaling(c, out x, out y, pivotArray);
ScaleToAverageEdgeLength(geometryGraph, x, y);
if (iter > 0)
{
AllPairsDistances apd = new AllPairsDistances(geometryGraph, false);
apd.Run();
double[][] d = apd.Result;
double[][] w = MultidimensionalScaling.ExponentialWeightMatrix(d, exponent);
// MultidimensionalScaling.DistanceScaling(d, x, y, w, iter);
MultidimensionalScaling.DistanceScalingSubset(d, x, y, w, iter);
}
}
/// <summary>
/// Computes the "stress" of the current layout of the given graph:
///
/// stress = sum_{(u,v) in V} D(u,v)^(-2) (d(u,v) - D(u,v))^2
///
/// where:
/// V is the set of nodes
/// d(u,v) is the euclidean distance between the centers of nodes u and v
/// D(u,v) is the graph-theoretic path length between u and v - scaled by average edge length.
///
/// The idea of “stress” in graph layout is that nodes that are immediate neighbors should be closer
/// together than nodes that are a few hops apart (i.e. that have path length>1). More generally
/// the distance between nodes in the drawing should be proportional to the path length between them.
/// The lower the “stress” score of a particular graph layout the better it conforms to this ideal.
///
/// </summary>
/// <param name="graph"></param>
/// <returns></returns>
public static double Stress(GeometryGraph graph)
{
ValidateArg.IsNotNull(graph, "graph");
double stress = 0;
if (graph.Edges.Count == 0)
{
return stress;
}
var apd = new AllPairsDistances(graph, false);
apd.Run();
var D = apd.Result;
double l = graph.Edges.Average(e => e.Length);
int i = 0;
foreach (var u in graph.Nodes)
{
int j = 0;
foreach (var v in graph.Nodes)
{
if (i != j)
{
double duv = (u.Center - v.Center).Length;
double Duv = l * D[i][j];
double d = Duv - duv;
stress += d * d / (Duv * Duv);
}
++j;
}
++i;
}
return stress;
}
/// <summary>
/// Layouts a connected graph with Multidimensional Scaling, using
/// shortest-path distances as Euclidean target distances.
/// </summary>
/// <param name="geometryGraph">A graph.</param>
/// <param name="settings">The settings for the algorithm.</param>
/// <param name="x">Coordinate vector.</param>
/// <param name="y">Coordinate vector.</param>
internal static void LayoutGraphWithMds(GeometryGraph geometryGraph, MdsLayoutSettings settings, out double[] x, out double[] y) {
x = new double[geometryGraph.Nodes.Count];
y = new double[geometryGraph.Nodes.Count];
if (geometryGraph.Nodes.Count == 0) return;
if (geometryGraph.Nodes.Count == 1)
{
x[0] = y[0] = 0;
return;
}
int k = Math.Min(settings.PivotNumber, geometryGraph.Nodes.Count);
int iter = settings.GetNumberOfIterationsWithMajorization(geometryGraph.Nodes.Count);
double exponent = settings.Exponent;
var pivotArray = new int[k];
PivotDistances pivotDistances = new PivotDistances(geometryGraph, false, pivotArray);
pivotDistances.Run();
double[][] c = pivotDistances.Result;
MultidimensionalScaling.LandmarkClassicalScaling(c, out x, out y, pivotArray);
ScaleToAverageEdgeLength(geometryGraph, x, y);
if (iter > 0) {
AllPairsDistances apd = new AllPairsDistances(geometryGraph, false);
apd.Run();
double[][] d = apd.Result;
double[][] w = MultidimensionalScaling.ExponentialWeightMatrix(d, exponent);
// MultidimensionalScaling.DistanceScaling(d, x, y, w, iter);
MultidimensionalScaling.DistanceScalingSubset(d, x, y, w, iter);
}
}
